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The lifespans of zebras in a particular zoo or normally distributed the average zebra lives 20.5 years the standard deviation is 3.9 years use the empirical rule to estimate the proper Millatti of a zebra living between 16.6 and 24.4 years

Respuesta :

Answer:

68% of the zebras have lifespan between 16.6 and 24.4 years.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 20.5 years

Standard Deviation, σ =  3.9 years

Empirical Formula:

  • Almost all the data lies within three standard deviations of the mean for a normally distributed data.
  • About 68% of data lies within one standard deviation of mean
  • About 95% of data lies within two standard deviation of the mean.
  • About 99.7% of data lies within three standard deviation of the mean.

We have to find the percentage of Zebras having lifespan between 16.6 and 24.4 years.

We can write:

[tex]16.6 = 20.5 - 3.9 = \mu -\sigma\\24.4 = 20.5 + 3.9 = \mu + \sigma[/tex]

Thus, by empirical rule around 68% of data lies within one standard deviation from the mean.

Thus, 68% of the zebras have lifespan between 16.6 and 24.4 years.

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